TSTP Solution File: SCT165+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:17:53 EDT 2023

% Result   : Theorem 27.88s 4.65s
% Output   : CNFRefutation 27.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   77 (  23 unt;   0 def)
%            Number of atoms       :  172 (  11 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  163 (  68   ~;  58   |;  14   &)
%                                         (   9 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-4 aty)
%            Number of variables   :  179 (  19 sgn; 119   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f56,axiom,
    ! [X14,X8,X11] :
      ( hBOOL(hAPP(hAPP(c_member(X11),X8),X14))
    <=> hBOOL(hAPP(X14,X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

fof(f63,axiom,
    ! [X9,X20] :
      ( X9 != X20
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X20))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(f93,axiom,
    ! [X14,X11] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X14),c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(f251,axiom,
    ! [X14,X11] :
      ( class_Finite__Set_Ofinite(X11)
     => c_Finite__Set_Ofinite(X11,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).

fof(f254,axiom,
    ! [X13,X14,X11] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X14),X13))
     => ( c_Finite__Set_Ofinite(X11,X13)
       => c_Finite__Set_Ofinite(X11,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(f257,axiom,
    ! [X11] :
      ( c_Finite__Set_Ofinite(tc_Option_Ooption(X11),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X11),tc_HOL_Obool)))
    <=> c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(f258,axiom,
    ! [X11] :
      ( class_Finite__Set_Ofinite(X11)
     => c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(f432,axiom,
    ! [X64,X17,X45,X11] :
      ( c_Finite__Set_Ofinite(X11,X45)
     => c_Finite__Set_Ofinite(X17,c_Set_Oimage(X11,X17,X64,X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(f469,axiom,
    ! [X17,X8,X1,X11] : hBOOL(hAPP(hAPP(c_member(X11),hAPP(X1,X8)),c_Set_Oimage(X17,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).

fof(f485,axiom,
    ! [X50] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X50)
    <=> ? [X4] :
        ! [X2] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X50))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(f517,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(f525,axiom,
    ! [X80,X11] : hAPP(c_COMBI(X11),X80) = X80,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(f575,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
    <=> hBOOL(hAPP(X0,X1)) ),
    inference(rectify,[],[f56]) ).

fof(f582,plain,
    ! [X0,X1] :
      ( X0 != X1
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
    inference(rectify,[],[f63]) ).

fof(f608,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rectify,[],[f93]) ).

fof(f764,plain,
    ! [X0,X1] :
      ( class_Finite__Set_Ofinite(X1)
     => c_Finite__Set_Ofinite(X1,X0) ),
    inference(rectify,[],[f251]) ).

fof(f766,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0))
     => ( c_Finite__Set_Ofinite(X2,X0)
       => c_Finite__Set_Ofinite(X2,X1) ) ),
    inference(rectify,[],[f254]) ).

fof(f769,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
    <=> c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
    inference(rectify,[],[f257]) ).

fof(f770,plain,
    ! [X0] :
      ( class_Finite__Set_Ofinite(X0)
     => c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
    inference(rectify,[],[f258]) ).

fof(f940,plain,
    ! [X0,X1,X2,X3] :
      ( c_Finite__Set_Ofinite(X3,X2)
     => c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
    inference(rectify,[],[f432]) ).

fof(f977,plain,
    ! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
    inference(rectify,[],[f469]) ).

fof(f993,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
    <=> ? [X1] :
        ! [X2] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
    inference(rectify,[],[f485]) ).

fof(f1008,plain,
    ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
    inference(rectify,[],[f525]) ).

fof(f1347,plain,
    ! [X0,X1] :
      ( c_Finite__Set_Ofinite(X1,X0)
      | ~ class_Finite__Set_Ofinite(X1) ),
    inference(ennf_transformation,[],[f764]) ).

fof(f1350,plain,
    ! [X0,X1,X2] :
      ( c_Finite__Set_Ofinite(X2,X1)
      | ~ c_Finite__Set_Ofinite(X2,X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
    inference(ennf_transformation,[],[f766]) ).

fof(f1351,plain,
    ! [X0,X1,X2] :
      ( c_Finite__Set_Ofinite(X2,X1)
      | ~ c_Finite__Set_Ofinite(X2,X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
    inference(flattening,[],[f1350]) ).

fof(f1354,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
      | ~ class_Finite__Set_Ofinite(X0) ),
    inference(ennf_transformation,[],[f770]) ).

fof(f1473,plain,
    ! [X0,X1,X2,X3] :
      ( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
      | ~ c_Finite__Set_Ofinite(X3,X2) ),
    inference(ennf_transformation,[],[f940]) ).

fof(f1528,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
    <=> ? [X1] :
        ! [X2] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
    inference(ennf_transformation,[],[f993]) ).

fof(f1604,plain,
    ! [X0,X1,X2] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
        | ~ hBOOL(hAPP(X0,X1)) )
      & ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ) ),
    inference(nnf_transformation,[],[f575]) ).

fof(f1605,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
        | X0 = X1 ) ),
    inference(nnf_transformation,[],[f582]) ).

fof(f1606,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
        | X0 = X1 ) ),
    inference(flattening,[],[f1605]) ).

fof(f1704,plain,
    ! [X0] :
      ( ( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) )
      & ( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ) ),
    inference(nnf_transformation,[],[f769]) ).

fof(f1793,plain,
    ! [X0] :
      ( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
        | ! [X1] :
          ? [X2] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
      & ( ? [X1] :
          ! [X2] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
        | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
    inference(nnf_transformation,[],[f1528]) ).

fof(f1794,plain,
    ! [X0] :
      ( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
        | ! [X1] :
          ? [X2] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
      & ( ? [X3] :
          ! [X4] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
        | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
    inference(rectify,[],[f1793]) ).

fof(f1795,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK41(X0,X1)),X1))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK41(X0,X1)),X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1796,plain,
    ! [X0] :
      ( ? [X3] :
        ! [X4] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
     => ! [X4] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1797,plain,
    ! [X0] :
      ( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
        | ! [X1] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK41(X0,X1)),X1))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK41(X0,X1)),X0)) ) )
      & ( ! [X4] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
        | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f1794,f1796,f1795]) ).

fof(f1934,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
    inference(cnf_transformation,[],[f1604]) ).

fof(f1935,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(cnf_transformation,[],[f1604]) ).

fof(f1949,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
    inference(cnf_transformation,[],[f1606]) ).

fof(f1998,plain,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(cnf_transformation,[],[f608]) ).

fof(f2237,plain,
    ! [X0,X1] :
      ( c_Finite__Set_Ofinite(X1,X0)
      | ~ class_Finite__Set_Ofinite(X1) ),
    inference(cnf_transformation,[],[f1347]) ).

fof(f2240,plain,
    ! [X2,X0,X1] :
      ( c_Finite__Set_Ofinite(X2,X1)
      | ~ c_Finite__Set_Ofinite(X2,X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
    inference(cnf_transformation,[],[f1351]) ).

fof(f2246,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
      | ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
    inference(cnf_transformation,[],[f1704]) ).

fof(f2247,plain,
    ! [X0] :
      ( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
      | ~ class_Finite__Set_Ofinite(X0) ),
    inference(cnf_transformation,[],[f1354]) ).

fof(f2467,plain,
    ! [X2,X3,X0,X1] :
      ( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
      | ~ c_Finite__Set_Ofinite(X3,X2) ),
    inference(cnf_transformation,[],[f1473]) ).

fof(f2516,plain,
    ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
    inference(cnf_transformation,[],[f977]) ).

fof(f2535,plain,
    ! [X0,X4] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
      | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
    inference(cnf_transformation,[],[f1797]) ).

fof(f2574,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(cnf_transformation,[],[f517]) ).

fof(f2582,plain,
    ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
    inference(cnf_transformation,[],[f1008]) ).

fof(f2621,plain,
    ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_resolution,[],[f1949]) ).

cnf(c_160,plain,
    ( ~ hBOOL(hAPP(X0,X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
    inference(cnf_transformation,[],[f1935]) ).

cnf(c_161,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
    | hBOOL(hAPP(X2,X1)) ),
    inference(cnf_transformation,[],[f1934]) ).

cnf(c_172,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
    inference(cnf_transformation,[],[f2621]) ).

cnf(c_218,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
    inference(cnf_transformation,[],[f1998]) ).

cnf(c_440,plain,
    ( ~ class_Finite__Set_Ofinite(X0)
    | c_Finite__Set_Ofinite(X0,X1) ),
    inference(cnf_transformation,[],[f2237]) ).

cnf(c_443,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1),X2))
    | ~ c_Finite__Set_Ofinite(X0,X2)
    | c_Finite__Set_Ofinite(X0,X1) ),
    inference(cnf_transformation,[],[f2240]) ).

cnf(c_448,plain,
    ( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
    | c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ),
    inference(cnf_transformation,[],[f2246]) ).

cnf(c_450,plain,
    ( ~ class_Finite__Set_Ofinite(X0)
    | c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
    inference(cnf_transformation,[],[f2247]) ).

cnf(c_667,plain,
    ( ~ c_Finite__Set_Ofinite(X0,X1)
    | c_Finite__Set_Ofinite(X2,c_Set_Oimage(X0,X2,X3,X1)) ),
    inference(cnf_transformation,[],[f2467]) ).

cnf(c_715,plain,
    hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,X2)),c_Set_Oimage(X3,X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),
    inference(cnf_transformation,[],[f2516]) ).

cnf(c_736,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X0),X1))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),sK42(X1))) ),
    inference(cnf_transformation,[],[f2535]) ).

cnf(c_773,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(cnf_transformation,[],[f2574]) ).

cnf(c_781,plain,
    hAPP(c_COMBI(X0),X1) = X1,
    inference(cnf_transformation,[],[f2582]) ).

cnf(c_38307,plain,
    hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),hAPP(X2,X3))),
    inference(superposition,[status(thm)],[c_715,c_161]) ).

cnf(c_46000,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK42(X0)),X0))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
    inference(superposition,[status(thm)],[c_736,c_172]) ).

cnf(c_49500,plain,
    hBOOL(hAPP(c_Set_Oimage(X0,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),X3)),
    inference(superposition,[status(thm)],[c_781,c_38307]) ).

cnf(c_53124,plain,
    ( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
    | c_Finite__Set_Ofinite(X0,X1) ),
    inference(superposition,[status(thm)],[c_218,c_443]) ).

cnf(c_53943,plain,
    ( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
    | c_Finite__Set_Ofinite(tc_Option_Ooption(X0),X1) ),
    inference(superposition,[status(thm)],[c_448,c_53124]) ).

cnf(c_54209,plain,
    ( ~ hBOOL(hAPP(X0,sK42(X0)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
    inference(superposition,[status(thm)],[c_160,c_46000]) ).

cnf(c_55026,plain,
    ( ~ class_Finite__Set_Ofinite(X0)
    | c_Finite__Set_Ofinite(tc_Option_Ooption(X0),X1) ),
    inference(superposition,[status(thm)],[c_440,c_53943]) ).

cnf(c_55299,plain,
    ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
    inference(superposition,[status(thm)],[c_49500,c_54209]) ).

cnf(c_55413,plain,
    ( ~ class_Finite__Set_Ofinite(X0)
    | c_Finite__Set_Ofinite(tc_Option_Ooption(tc_Option_Ooption(X0)),X1) ),
    inference(superposition,[status(thm)],[c_55026,c_53943]) ).

cnf(c_55758,plain,
    ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
    inference(superposition,[status(thm)],[c_667,c_55299]) ).

cnf(c_56849,plain,
    ~ class_Finite__Set_Ofinite(X0),
    inference(global_subsumption_just,[status(thm)],[c_55413,c_450,c_55758]) ).

cnf(c_56851,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_773,c_56849]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16  % Problem  : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.17  % Command  : run_iprover %s %d THM
% 0.14/0.37  % Computer : n003.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug 24 15:08:53 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.19/0.45  Running first-order theorem proving
% 0.19/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.88/4.65  % SZS status Started for theBenchmark.p
% 27.88/4.65  % SZS status Theorem for theBenchmark.p
% 27.88/4.65  
% 27.88/4.65  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.88/4.65  
% 27.88/4.65  ------  iProver source info
% 27.88/4.65  
% 27.88/4.65  git: date: 2023-05-31 18:12:56 +0000
% 27.88/4.65  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.88/4.65  git: non_committed_changes: false
% 27.88/4.65  git: last_make_outside_of_git: false
% 27.88/4.65  
% 27.88/4.65  ------ Parsing...
% 27.88/4.65  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 27.88/4.65  
% 27.88/4.65  ------ Preprocessing... sup_sim: 24  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e  sup_sim: 24  sf_s  rm: 21 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 21 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 21 0s  sf_e  pe_s  pe_e 
% 27.88/4.65  
% 27.88/4.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 27.88/4.65  
% 27.88/4.65  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 27.88/4.65  ------ Proving...
% 27.88/4.65  ------ Problem Properties 
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  clauses                                 435
% 27.88/4.65  conjectures                             0
% 27.88/4.65  EPR                                     19
% 27.88/4.65  Horn                                    332
% 27.88/4.65  unary                                   111
% 27.88/4.65  binary                                  151
% 27.88/4.65  lits                                    1109
% 27.88/4.65  lits eq                                 245
% 27.88/4.65  fd_pure                                 0
% 27.88/4.65  fd_pseudo                               0
% 27.88/4.65  fd_cond                                 11
% 27.88/4.65  fd_pseudo_cond                          72
% 27.88/4.65  AC symbols                              0
% 27.88/4.65  
% 27.88/4.65  ------ Schedule dynamic 5 is on 
% 27.88/4.65  
% 27.88/4.65  ------ no conjectures: strip conj schedule 
% 27.88/4.65  
% 27.88/4.65  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  ------ 
% 27.88/4.65  Current options:
% 27.88/4.65  ------ 
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  ------ Proving...
% 27.88/4.65  
% 27.88/4.65  
% 27.88/4.65  % SZS status Theorem for theBenchmark.p
% 27.88/4.65  
% 27.88/4.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.88/4.65  
% 27.88/4.65  
%------------------------------------------------------------------------------